Solve -x^2 8x-12=0

Question

Solve the equation

x = - \frac{3 12}{2}

Alternative Form

x \approx - 1.144714

Evaluate

- x^{2} \times 8 x - 12 = 0

Multiply

More Steps

Evaluate

- x^{2} \times 8 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 8

Add the numbers

- x^{3} \times 8

Use the commutative property to reorder the terms

- 8 x^{3}

- 8 x^{3} - 12 = 0

Move the constant to the right-hand side and change its sign

- 8 x^{3} = 0 + 12

Removing 0 doesn't change the value,so remove it from the expression

- 8 x^{3} = 12

Change the signs on both sides of the equation

8 x^{3} = - 12

Divide both sides

\frac{8 x ^{3}}{8} = \frac{- 12}{8}

Divide the numbers

x^{3} = \frac{- 12}{8}

Divide the numbers

More Steps

Evaluate

\frac{- 12}{8}

Cancel out the common factor 4

\frac{- 3}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{3}{2}

x^{3} = - \frac{3}{2}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{3}{2}

Calculate

x = 3 - \frac{3}{2}

Solution

More Steps

Evaluate

3 - \frac{3}{2}

An odd root of a negative radicand is always a negative

- 3 \frac{3}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

- \frac{3 3}{3 2}

Multiply by the Conjugate

\frac{- 3 3 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{- 3 3 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 33 \times 34

The product of roots with the same index is equal to the root of the product

- 3 3 \times 4

Calculate the product

- 312

\frac{- 3 12}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

The product of roots with the same index is equal to the root of the product

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{- 3 12}{2}

Calculate

- \frac{3 12}{2}

x = - \frac{3 12}{2}

Alternative Form

x \approx - 1.144714

Show Solution